Finite-difference solution of the eikonal equation for
transversely isotropic media

David W.S. Eaton

ABSTRACT

A new finite-difference technique is presented for solving the eikonal equation
for inhomogeneous, transversely isotropic media. The method is an extension of
other recently developed, isotropic finite-difference algorithms. An expanding-wavefront
scheme on a triangular mesh of points is employed, in order to ensure
causality and minimize grid anisotropy. Several examples are presented to illustrate
the method for varying degrees of anisotropy and inhomogeneity. This technique is
particularly well suited to tomographic and migration/inversion applications, since
the traveltimes can be efficiently calculated on a dense grid of points for a smoothly
varying background.